Finite Group Databasebeta

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C3×D5×D539 #44568385

order32340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D539
unambiguous semidirect product(D5×C11)⋊(C3×D49)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C22
derived, HallC5×C11×C49 ⋊ C22×C3
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×C3×D5
HallC5×C49 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3×D49
SylowC49 ⋊ C3×D5×D11
HallC3×C11 ⋊ D5×D49
HallC3×C5 ⋊ C2×D539
SylowC11 ⋊ C3×D5×D49
SylowC5 ⋊ C2×C3×D539

Subgroups

subgroupG/H
center, hypercenterC3D5×D539
commutator, cosocle, hypocenterC5×C11×C49C22×C3
FrattiniC7C3×D5×D77
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C2×D7
LCSG ▷ C5×C11×C49
UCSC1 ◁ C3

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 87);